Find general non-constant solution for differential equation

eqn=diff(y(t),t) == k*y*(1-y/M);
S=dsolve(eqn);
Sz = S(3) %general non-constant solution
>> Sz = M/(exp(-M*(C1 + (k*t)/M)) + 1)

If I put my code in matlab, for Sz I get an 3x1 array with

S(1) = 0

S(2) = M

S(3) = M/(exp(-M*(C1 + (k*t)/M)) + 1)

Now I know the solution to this problem is in S(3) as seen in the code, but is there a way how Matlab can find the solution without me looking into the array of Sz?

Thanks!

Answer 1

[Ameer Hamza]

All three solution given by dsolve() satisfies the differential equation. So, I guess you want to get the solution which depends on time. You can do it like this

syms y(t) M k
eqn=diff(y(t),t) == k*y*(1-y/M);
S=dsolve(eqn);

idx = arrayfun(@(x) ismember(t, symvar(x)), S);
S = S(idx);

[Borjan Trajanoski]

Thank you, that helped me very much!

[Ameer Hamza]

I am glad to be of help.